So, what really characterizes ALPs is the trilinear \(\gamma \) -\(\gamma \) -\(a\)  vertex described by the last term in \({\cal L}_{\rm ALP}\) , whereby one ALP couples to two photons. Owing to this vertex, ALPs can be emitted by astronomical objects of various kinds, and the present situation can be summarized as follows. The negative result of the CAST experiment designed to detect ALPs emitted by the Sun yields the bound \(M > 0.86 \cdot 10^{10} \, {\rm GeV}\)  for
\(m < 0.02 \, {\rm eV}\)  [1]}. Moreover, theoretical considerations concerning star cooling via ALP emission provide the generic bound \(M > 10^{10} \, {\rm GeV}\) , which for \(m < 10^{- 10} \, {\rm eV}\)  gets replaced by the stronger one \(M > 10^{11} \, {\rm GeV}\)  even if with a large uncertainty [2]}. The same \(\gamma \) -\(\gamma \) -\(a\)  vertex produces an off-diagonal element in the mass matrix for the photon-ALP system in the presence of an external magnetic field \({\bf B}\) . Therefore, the interaction eigenstates differ from the propagation eigenstates and photon-ALP oscillations show up [3]}.
